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The Talismans themselves don't drop as loot but the recipe for Talismans are dropped as regular loot.

Talismans may be received by gambling at the transmutation station:
3 Uncommon/green gives an Uncommon/green Talisman or a chance for a Rare/yellow Talisman.
3 Rare/yellow gives an Uncommon/green Talisman or a chance for a Legendary/purple Talisman.

The Trigger rate is random when the Uncommon/green Talisman transmutes into a Rare/yellow or the Rare/yellow transmutes into a Legendary/purple.
3 of the same Trigger Rate keeps the same Trigger rate.

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